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This is a delightful question. You could try doing this at the equator, but that would be your worst choice. The equator is about 25,000 miles long, so you would have to go at a brisk 25,000 miles per hour to stay in daylight without losing gound at all. On the other extreme, during a polar summer you could relax and not move at all. I think what you would have to do is find a circuit just south of the arctic region, so you could avoid the perpetual night of winter. As long as you are at a latitude where there is always a sunrise, you could scoot around the globe at a much slower clip than 25,000 miles per hour, and always be in sunlight. Or you could hop over the arctic circle during the summer, (for rest and re-fueling?) and hop back below it and start zipping around when the sun starts to set. The arctic circle almost touches the northern-most tip of Iceland. A latitude at or just south of the circle would be ideal. With some quick-and-dirty trig, I calculated the length of the arctic circle to be roughly 9,930 miles. So if you travel roughly 9,930 miles per hour just about at the arctic circle, you should maintain sunlight (or darkness) all the time.

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Q: How fast would you have to move to stay in daylight all the time?
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